One corner of a triangle is 2 times the other and 25 degrees less than the third. Find all the corners of the triangle.
September 21, 2021 | education
| 1. Let’s denote the angles of the triangle by A, B and C.
Then the first equation: A + B + C = 180 o.
2. By the condition of the problem, A = 2 * B (second equation) and A = C – 25 o (third equation).
3. From the third equation, taking into account the second: C = A + 25 = 2 * B + 25.
4. Substitute the expressions for A and C in the first equation. We get:
2 * B + B + 2 * B + 25 = 5 * B + 25 = 180. Hence B = 155/5 = 31 p.
5. Therefore, A = 2 * B = 2 * 31 = 62 o, and C = A + 25 = 62 + 25 = 87 o.
Answer: the angles of the triangle have the following meanings: A = 31 o, B = 62 o, C = 87 o.
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